Mark position determination method

Abstract

A method of determining positions of marks, the marks comprising periodic structures, at least some of the structures comprising periodic sub-structures, the sub-structures having a smaller period than the structures, the marks formed with positional offsets between the sub-structures and structures, the positional offsets caused by a combination of both known and unknown components, the method comprising illuminating a plurality of the marks with radiation having different characteristics, detecting radiation diffracted by the marks using one or more detectors which produce output signals, discriminating between constituent parts of the signals, the discriminating based on a variation of the signals as a function of spatial positions of the marks on a substrate, selecting at least one of the constituent parts of the signals, and using the at least one selected constituent part, and information relating to differences between the known components, to calculate a corrected position of at least one mark.

The invention claimed is: 
     
       1. A method of determining positions of marks on a substrate, the marks comprising structures arranged periodically in at least a first direction, at least some of the structures comprising periodic sub-structures, the sub-structures having a smaller period than the structures, the marks being formed with positional offsets between the sub-structures and the structures, the positional offsets being caused by a combination of both known and unknown components, the method comprising:
 illuminating a plurality of the marks with radiation; 
 detecting radiation which is diffracted by the marks and which has different characteristics, using one or more detectors which produce output signals; 
 processing the signals, wherein the processing comprises discriminating between constituent parts of each of the signals, the discriminating being based on a variation of the signals as a function of spatial positions of the marks on the substrate; 
 selecting at least one of the constituent parts of the signals that represents a higher spatial frequency variation in measured positions of the marks as a function of spatial positions of the marks on the substrate than a constituent part that is not selected; and 
 using the at least one selected constituent part, and information relating to a difference between the known components, to calculate a corrected position of at least one mark. 
 
     
     
       2. The method of  claim 1 , further comprising performing a validation, the validation comprising comparing constituent parts of signals that were not selected, the signals originating from radiation diffracted from marks which are adjacent to each other. 
     
     
       3. The method of  claim 1 , wherein the processing comprises applying principal component analysis or independent component analysis or blind signal separation or polynomial fitting, to the signals. 
     
     
       4. The method of  claim 1 , wherein the calculation uses a relationship between the output signals and the positional offsets of the marks. 
     
     
       5. The method of  claim 4 , wherein the relationship has the same form for radiation having different characteristics. 
     
     
       6. The method of  claim 4 , wherein the relationship is a linear relationship. 
     
     
       7. The method of  claim 1 , wherein the different characteristics of the diffracted radiation are provided by illuminating the plurality of marks with radiation comprising different wavelengths or different polarizations. 
     
     
       8. The method of  claim 1 , wherein the different characteristics of the diffracted radiation are provided by illuminating the plurality of marks with different off-axis radiation beams and/or by detecting different diffraction orders. 
     
     
       9. The method of  claim 8 , wherein the one or more detectors comprises an image sensor. 
     
     
       10. The method of  claim 1 , wherein at least one selected constituent part of the signals comprises a constituent part of the signals with spatial variation associated with a radiation exposure path across the substrate. 
     
     
       11. A lithographic apparatus comprising:
 a patterning subsystem configured to transfer a pattern to a substrate; 
 a measuring subsystem configured to measure positions of the substrate in relation to the patterning subsystem, 
 wherein the patterning subsystem is arranged to use the positions measured by the measuring subsystem to apply the pattern at a desired position on the substrate and wherein the measuring subsystem is arranged to position the applied pattern by reference to measured positions of marks provided on the substrate and wherein the measuring subsystem is arranged to calculate the measured positions of the marks by the method as claimed in  claim 1 . 
 
     
     
       12. A method of manufacturing devices wherein a device pattern is applied to a substrate using a lithographic process, the method including positioning the applied pattern by reference to measured positions of one or more marks formed on the substrate, the measured positions being obtained by the method as claimed in  claim 1 . 
     
     
       13. A non-transitory computer program product comprising machine-readable instructions therein, the instructions, upon execution by a processing device, configured to cause the processing device to at least:
 obtain signals that correspond to detection of radiation, diffracted by marks on a substrate, having different characteristics, the marks comprising structures arranged periodically, at least some of the structures comprising periodic sub-structures, the sub-structures having a smaller period than the structures, and the marks formed with positional offsets between the sub-structures and the structures, the positional offsets caused by a combination of both known and unknown components; discriminate between constituent parts of each of the signals, the discriminating based on a variation of the signals as a function of spatial positions of the marks on the substrate and at least one constituent part representing a different type of error in physical manufacturing or processing of the marks than another at least constituent part; 
 select at least one of the constituent parts of the signals; and 
 use the at least one selected constituent part of the signals, and information relating to differences between the known components, to calculate a corrected position of at least one mark. 
 
     
     
       14. A non-transitory computer program product comprising machine-readable instructions therein, the instructions, upon execution by a processing device, configured to cause the processing device to at least:
 obtain signals from one or more detectors, which signals correspond to detection of radiation, diffracted by marks on a substrate, having different characteristics, the marks comprising structures arranged periodically, at least some of the structures comprising periodic sub-structures, the sub-structures having a smaller period than the structures, and the marks formed with positional offsets between the sub-structures and the structures, the positional offsets caused by a combination of both known and unknown components; 
 process the signals, wherein processing of the signals comprises discriminating between constituent parts of each of the signals, the discriminating based on a variation of the signals as a function of spatial positions of the marks on the substrate; 
 select at least one of the constituent parts of the signals that represents a higher spatial frequency variation in measured positions of the marks as a function of spatial positions of the marks on the substrate than a constituent part that is not selected; and 
 use the at least one selected constituent part, and information relating to a difference between the known components, to calculate a corrected position of at least one mark. 
 
     
     
       15. The computer program product of  claim 14 , wherein the instructions are further configured to cause the processing device to perform a validation, the validation comprising comparison of constituent parts of signals that were not selected, the signals originating from radiation diffracted from marks which are adjacent to each other. 
     
     
       16. The computer program product of  claim 14 , wherein the calculation uses a relationship between the output signals and the positional offsets of the marks. 
     
     
       17. The computer program product of  claim 16 , wherein the relationship has the same form for radiation having different characteristics. 
     
     
       18. The computer program product of  claim 17 , wherein the relationship is a linear relationship. 
     
     
       19. The computer program product of  claim 14 , wherein the different characteristics of the diffracted radiation are provided by illuminating the plurality of marks with radiation comprising different wavelengths or different polarizations, by illuminating the plurality of marks with radiation comprising different off-axis radiation beams, and/or by detecting different diffraction orders. 
     
     
       20. The computer program product of  claim 14 , wherein at least one selected constituent part of the signals comprises a constituent part of the signals with spatial variation associated with a radiation exposure path across the substrate. 
     
     
       21. An apparatus comprising:
 an optical system configured to illuminate a plurality of marks on a substrate with radiation, and detect radiation which is diffracted by the marks using one or more detectors which produce signals; and 
 the non-transitory computer program product of  claim 13 .